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Initially the earth was a fire-ball, slo...

Initially the earth was a fire-ball, slowly it has cooled to form earth crust and its different layers. At the beginning `""_(92)^(238)U` was present and no `""_(82)^(206)` Pb was there. With the passage of time, uranium decayed to `""_(82)^(206)Pb` The decay process is : ` ""_(92)^(238)U underset((x alpha, y beta))to ""_(82)^(206)Pb , t_(1//2)` of `""^(238)U = 4.5 xx 10^(9)` yrs
A sample of rock from south America contains equal number of atoms of `""^(238)U and ""^(206)Pb`. The age of the rock will be :

A

`4. 5 xx 10^(9)` years

B

`9 xx 10^(9)` years

C

`13.5 xx 10^(9)` years

D

`2.25 xx 10^(9)` years

Text Solution

Verified by Experts

The correct Answer is:
A
`(0.693)/(t_(1//2)) = (2.303)/(t_("age")) log ((N_(0))/(N)), " " (0.693)/(4.5 xx 10^(9)) = (2.303)/(t_("age")) log "" ((2)/(1))`
`t_("age") = 4.5 xx 10^(9)` yrs, `N_(0) = 1+ 1 = 2, N = 1`
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